Subgroups — #31063442

Order 17152.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568494	C₂	1	1	yes	maximal, characteristic
2	#22568494	C₂	1	1	yes	maximal, characteristic
3	#22568176	C₂	1	1	yes	maximal, characteristic, complemented
4	#22567979	C₂	1	1	yes	maximal, characteristic, complemented
5	#22567974	C₂	1	1	yes	maximal, characteristic, complemented
6	#22567956	C₂	1	1	yes	maximal, characteristic, complemented
7	#22567952	C₂	1	1	yes	maximal, characteristic, complemented
8	#22567693	C₂	1	1	yes	maximal, characteristic, complemented
9	#22567690	C₂	1	1	yes	maximal, characteristic, complemented
10	#22567625	C₂	1	1	yes	maximal, characteristic, complemented
11	#22567335	C₂	1	1	yes	maximal, characteristic, complemented
12	#22567192	C₂	1	1	yes	maximal, characteristic, complemented
13	#22567188	C₂	1	1	yes	maximal, characteristic, complemented
14	#22567093	C₂	1	1	yes	maximal, characteristic, complemented
15	#22567086	C₂	1	1	yes	maximal, characteristic, complemented
16	#22566868	C₂	1	1	yes	maximal, characteristic, complemented
17	#22566864	C₂	1	1	yes	maximal, characteristic, complemented
18	#22566521	C₂	1	1	yes	maximal, characteristic, complemented
19	#22566018	C₂	1	1	yes	maximal, characteristic
20	#22566018	C₂	1	1	yes	maximal, characteristic
21	#22565434	C₂	1	1	yes	maximal, characteristic, complemented
22	#22565428	C₂	1	1	yes	maximal, characteristic, complemented
23	#22565221	C₂	1	1	yes	maximal, characteristic, complemented
24	#22565215	C₂	1	1	yes	maximal, characteristic, complemented
25	#22563934	C₂	1	1	yes	maximal, characteristic, complemented
26	#22563933	C₂	1	1	yes	maximal, characteristic, complemented
27	#22563912	C₂	1	1	yes	maximal, characteristic, complemented
28	#22563911	C₂	1	1	yes	maximal, characteristic, complemented
29	#22562807	C₂	1	1	yes	maximal, characteristic
30	C₂×#16863271	C₂	1	1	yes	maximal, characteristic
31	C₆₇×#2312	C₂	1	1	yes	maximal, characteristic
32	C₂⁴×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14524035	C₂²	1	1	yes	characteristic, complemented
36	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
37	C₂×#14524020	C₂²	1	1	yes	characteristic
38	C₂×#14524020	C₂²	1	1	yes	characteristic
39	C₂×#14524020	C₂²	1	1	yes	characteristic
40	C₂×#14524020	C₂²	1	1	yes	characteristic
41	C₂×#14524020	C₂²	1	1	yes	characteristic
42	C₂×#14524020	C₂²	1	1	yes	characteristic
43	C₂×#14524020	C₂²	1	1	yes	characteristic
44	C₂×#14524020	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
48	#16863338	C₂²	1	1	yes	characteristic, complemented
49	#16863338	C₂²	1	1	yes	characteristic, complemented
50	#16863338	C₂²	1	1	yes	characteristic, complemented
51	#16863338	C₂²	1	1	yes	characteristic, complemented
52	#16863338	C₂²	1	1	yes	characteristic, complemented
53	#16863338	C₂²	1	1	yes	characteristic, complemented
54	#16863335	C₂²	1	1	yes	characteristic, complemented
55	#16863335	C₂²	1	1	yes	characteristic, complemented
56	#16863332	C₂²	1	1	yes	characteristic
57	#16863332	C₂²	1	1	yes	characteristic
58	#16863332	C₂²	1	1	yes	characteristic
59	#16863332	C₂²	1	1	yes	characteristic
60	#16863330	C₂²	1	1	yes	characteristic, complemented
61	#16863330	C₂²	1	1	yes	characteristic, complemented
62	#16863330	C₂²	1	1	yes	characteristic, complemented
63	#16863330	C₂²	1	1	yes	characteristic, complemented
64	#16863330	C₂²	1	1	yes	characteristic, complemented
65	#16863330	C₂²	1	1	yes	characteristic, complemented
66	#16863329	C₂²	1	1	yes	characteristic, complemented
67	#16863329	C₂²	1	1	yes	characteristic, complemented
68	#16863329	C₂²	1	1	yes	characteristic, complemented
69	#16863329	C₂²	1	1	yes	characteristic, complemented
70	#16863328	C₂²	1	1	yes	characteristic, complemented
71	#16863328	C₂²	1	1	yes	characteristic, complemented
72	#16863328	C₂²	1	1	yes	characteristic, complemented
73	#16863328	C₂²	1	1	yes	characteristic, complemented
74	#16863328	C₂²	1	1	yes	characteristic, complemented
75	#16863328	C₂²	1	1	yes	characteristic, complemented
76	#16863319	C₂²	1	1	yes	characteristic
77	#16863319	C₂²	1	1	yes	characteristic
78	#16863319	C₂²	1	1	yes	characteristic
79	#16863319	C₂²	1	1	yes	characteristic
80	#16863319	C₂²	1	1	yes	characteristic
81	#16863319	C₂²	1	1	yes	characteristic
82	#16863319	C₂²	1	1	yes	characteristic
83	#16863319	C₂²	1	1	yes	characteristic
84	#16863317	C₂²	1	1	yes	characteristic, complemented
85	#16863317	C₂²	1	1	yes	characteristic, complemented
86	#16863317	C₂²	1	1	yes	characteristic, complemented
87	#16863317	C₂²	1	1	yes	characteristic, complemented
88	#16863317	C₂²	1	1	yes	characteristic, complemented
89	#16863317	C₂²	1	1	yes	characteristic, complemented
90	#16863316	C₂²	1	1	yes	characteristic, complemented
91	#16863316	C₂²	1	1	yes	characteristic, complemented
92	#16863308	C₂²	1	1	yes	characteristic
93	#16863308	C₂²	1	1	yes	characteristic
94	#16863308	C₂²	1	1	yes	characteristic
95	#16863308	C₂²	1	1	yes	characteristic
96	#16863302	C₂²	1	1	yes	characteristic, complemented
97	#16863302	C₂²	1	1	yes	characteristic, complemented
98	#16863300	C₂²	1	1	yes	characteristic, complemented
99	#16863300	C₂²	1	1	yes	characteristic, complemented
100	#16863295	C₂²	1	1	yes	characteristic, complemented
101	#16863295	C₂²	1	1	yes	characteristic, complemented
102	#16863294	C₂²	1	1	yes	characteristic, complemented
103	#16863294	C₂²	1	1	yes	characteristic, complemented
104	#16863294	C₂²	1	1	yes	characteristic, complemented
105	#16863294	C₂²	1	1	yes	characteristic, complemented
106	#16863294	C₂²	1	1	yes	characteristic, complemented
107	#16863294	C₂²	1	1	yes	characteristic, complemented
108	#16863293	C₂²	1	1	yes	characteristic, complemented
109	#16863293	C₂²	1	1	yes	characteristic, complemented
110	#16863292	C₂²	1	1	yes	characteristic, complemented
111	#16863292	C₂²	1	1	yes	characteristic, complemented
112	#16863289	C₂²	1	1	yes	characteristic
113	#16863289	C₂²	1	1	yes	characteristic
114	#16863289	C₂²	1	1	yes	characteristic
115	#16863289	C₂²	1	1	yes	characteristic
116	#16863289	C₂²	1	1	yes	characteristic
117	#16863289	C₂²	1	1	yes	characteristic
118	#16863289	C₂²	1	1	yes	characteristic
119	#16863289	C₂²	1	1	yes	characteristic
120	#16863283	C₂²	1	1	yes	characteristic, complemented
121	#16863283	C₂²	1	1	yes	characteristic, complemented
122	#16863280	C₂²	1	1	yes	characteristic, complemented
123	#16863280	C₂²	1	1	yes	characteristic, complemented
124	#16863280	C₂²	1	1	yes	characteristic, complemented
125	#16863280	C₂²	1	1	yes	characteristic, complemented
126	#16863279	C₂²	1	1	yes	characteristic, complemented
127	#16863279	C₂²	1	1	yes	characteristic, complemented
128	#16863271	C₂²	1	1	yes	characteristic
129	#16863271	C₂²	1	1	yes	characteristic
130	#16863271	C₂²	1	1	yes	characteristic
131	#16863271	C₂²	1	1	yes	characteristic
132	#16863271	C₂²	1	1	yes	characteristic
133	#16863271	C₂²	1	1	yes	characteristic
134	#16863271	C₂²	1	1	yes	characteristic
135	#16863271	C₂²	1	1	yes	characteristic
136	#16863271	C₂²	1	1	yes	characteristic
137	#16863271	C₂²	1	1	yes	characteristic
138	#16863271	C₂²	1	1	yes	characteristic
139	#16863271	C₂²	1	1	yes	characteristic
140	#16863271	C₂²	1	1	yes	characteristic
141	#16863271	C₂²	1	1	yes	characteristic
142	#16863271	C₂²	1	1	yes	characteristic
143	#16863271	C₂²	1	1	yes	characteristic
144	#16863268	C₂²	1	1	yes	characteristic
145	#16863268	C₂²	1	1	yes	characteristic
146	#16863268	C₂²	1	1	yes	characteristic
147	#16863268	C₂²	1	1	yes	characteristic
148	#16863268	C₂²	1	1	yes	characteristic
149	#16863268	C₂²	1	1	yes	characteristic
150	#16863268	C₂²	1	1	yes	characteristic
151	#16863268	C₂²	1	1	yes	characteristic
152	#16863266	C₂²	1	1	yes	characteristic, complemented
153	#16863265	C₂²	1	1	yes	characteristic, complemented
154	#16863262	C₂²	1	1	yes	characteristic, complemented
155	#16863261	C₂²	1	1	yes	characteristic, complemented
156	#16863256	C₂²	1	1	yes	characteristic
157	#16863256	C₂²	1	1	yes	characteristic
158	#16863254	C₂²	1	1	yes	characteristic
159	#16863254	C₂²	1	1	yes	characteristic
160	#16863254	C₂²	1	1	yes	characteristic
161	#16863254	C₂²	1	1	yes	characteristic
162	#16863254	C₂²	1	1	yes	characteristic
163	#16863254	C₂²	1	1	yes	characteristic
164	#16863254	C₂²	1	1	yes	characteristic
165	#16863254	C₂²	1	1	yes	characteristic
166	#16863252	C₂²	1	1	yes	characteristic
167	#16863252	C₂²	1	1	yes	characteristic
168	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic
170	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
171	C₂×C₆₇⋊#95	C₂²	1	1	yes	characteristic
172	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
173	#388×C₆₇	C₂²	1	1	yes	characteristic
174	#388×C₆₇	C₂²	1	1	yes	characteristic
175	#388×C₆₇	C₂²	1	1	yes	characteristic
176	#388×C₆₇	C₂²	1	1	yes	characteristic
177	#388×C₆₇	C₂²	1	1	yes	characteristic
178	#388×C₆₇	C₂²	1	1	yes	characteristic
179	#388×C₆₇	C₂²	1	1	yes	characteristic
180	#388×C₆₇	C₂²	1	1	yes	characteristic
181	#380×C₆₇	C₂²	1	1	yes	characteristic
182	#380×C₆₇	C₂²	1	1	yes	characteristic
183	#379×C₆₇	C₂²	1	1	yes	characteristic
184	#379×C₆₇	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
191	C₂³×Dic₆₇	—	4	2	no	—
192	C₂³×Dic₆₇	—	4	2	no	—
193	C₂³×Dic₆₇	—	4	2	no	—
194	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
195	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
196	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
202	#14524043	—	4	2	no	—
203	#14524042	—	4	2	no	—
204	#14524035	—	4	2	no	—
205	#14524034	—	4	2	no	—
206	#14524020	—	4	2	no	—
207	#14524020	—	4	2	no	—
208	#14524020	—	4	2	no	—
209	#14524020	—	4	2	no	—
210	#14524020	—	4	2	no	—
211	#14524020	—	4	2	no	—
212	#14524020	—	4	2	no	—
213	#14524020	—	4	2	no	—
214	C₂×C₄⋊Dic₆₇	—	4	2	no	—
215	C₂×C₄⋊Dic₆₇	—	4	2	no	—
216	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₆₇	—	4	2	no	—
265	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
285	C₆₇⋊#95	C₂³	1	1	yes	characteristic
286	C₆₇⋊#95	C₂³	1	1	yes	characteristic
287	C₆₇⋊#95	C₂³	1	1	yes	characteristic
288	C₆₇⋊#95	C₂³	1	1	yes	characteristic
289	C₆₇⋊#95	C₂³	1	1	yes	characteristic
290	C₆₇⋊#95	C₂³	1	1	yes	characteristic
291	C₆₇⋊#95	C₂³	1	1	yes	characteristic
292	C₆₇⋊#95	C₂³	1	1	yes	characteristic
293	C₆₇⋊#95	C₂³	1	1	yes	characteristic
294	C₆₇⋊#95	C₂³	1	1	yes	characteristic
295	C₆₇⋊#95	C₂³	1	1	yes	characteristic
296	C₆₇⋊#95	C₂³	1	1	yes	characteristic
297	C₆₇⋊#95	C₂³	1	1	yes	characteristic
298	C₆₇⋊#95	C₂³	1	1	yes	characteristic
299	C₆₇⋊#95	C₂³	1	1	yes	characteristic
300	C₆₇⋊#95	C₂³	1	1	yes	characteristic
301	C₆₇⋊#95	C₂³	1	1	yes	characteristic
302	C₆₇⋊#95	C₂³	1	1	yes	characteristic
303	C₆₇⋊#95	C₂³	1	1	yes	characteristic
304	C₆₇⋊#95	C₂³	1	1	yes	characteristic
305	C₆₇⋊#95	C₂³	1	1	yes	characteristic
306	C₆₇⋊#95	C₂³	1	1	yes	characteristic
307	C₆₇⋊#95	C₂³	1	1	yes	characteristic
308	C₆₇⋊#95	C₂³	1	1	yes	characteristic
309	C₆₇⋊#95	C₂³	1	1	yes	characteristic
310	C₆₇⋊#95	C₂³	1	1	yes	characteristic
311	C₆₇⋊#95	C₂³	1	1	yes	characteristic
312	C₆₇⋊#95	C₂³	1	1	yes	characteristic
313	C₆₇⋊#95	C₂³	1	1	yes	characteristic
314	C₆₇⋊#95	C₂³	1	1	yes	characteristic
315	C₆₇⋊#95	C₂³	1	1	yes	characteristic
316	C₆₇⋊#95	C₂³	1	1	yes	characteristic
317	C₆₇⋊#95	C₂³	1	1	yes	characteristic
318	C₆₇⋊#95	C₂³	1	1	yes	characteristic
319	C₆₇⋊#95	C₂³	1	1	yes	characteristic
320	C₆₇⋊#95	C₂³	1	1	yes	characteristic
321	C₆₇⋊#95	C₂³	1	1	yes	characteristic
322	C₆₇⋊#95	C₂³	1	1	yes	characteristic
323	C₆₇⋊#95	C₂³	1	1	yes	characteristic
324	C₆₇⋊#95	C₂³	1	1	yes	characteristic
325	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
326	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₆₇	Q₈	1	8	yes	complemented
333	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
353	#95×C₆₇	C₂³	1	1	yes	characteristic
354	#95×C₆₇	C₂³	1	1	yes	characteristic
355	#95×C₆₇	C₂³	1	1	yes	characteristic
356	#95×C₆₇	C₂³	1	1	yes	characteristic
357	#95×C₆₇	C₂³	1	1	yes	characteristic
358	#95×C₆₇	C₂³	1	1	yes	characteristic
359	#95×C₆₇	C₂³	1	1	yes	characteristic
360	#95×C₆₇	C₂³	1	1	yes	characteristic
361	C₂×Dic₁₃₄	—	2	2	no	—
362	C₂×Dic₁₃₄	—	2	2	no	—
363	C₂×Dic₁₃₄	—	4	1	no	—
364	C₂×Dic₁₃₄	—	4	1	no	—
365	C₂×Dic₁₃₄	—	4	1	no	—
366	C₂×Dic₁₃₄	—	4	1	no	—
367	C₂×Dic₁₃₄	—	4	1	no	—
368	C₂×Dic₁₃₄	—	4	1	no	—
369	C₂×Dic₁₃₄	—	4	1	no	—
370	C₂×Dic₁₃₄	—	4	1	no	—
371	C₂×Dic₁₃₄	—	4	1	no	—
372	C₂×Dic₁₃₄	—	4	1	no	—
373	C₂²×Dic₆₇	—	2	2	no	—
374	C₂²×Dic₆₇	—	2	2	no	—
375	C₂²×Dic₆₇	—	2	2	no	—
376	C₂²×Dic₆₇	—	2	2	no	—
377	C₂²×Dic₆₇	—	2	2	no	—
378	C₂²×Dic₆₇	—	2	2	no	—
379	C₂²×Dic₆₇	—	2	2	no	—
380	C₂²×Dic₆₇	—	2	2	no	—
381	C₂²×Dic₆₇	—	2	2	no	—
382	C₂²×Dic₆₇	—	2	2	no	—
383	C₂²×Dic₆₇	—	4	1	no	—
384	C₂²×Dic₆₇	—	4	1	no	—
385	C₂²×Dic₆₇	—	4	1	no	—
386	C₂²×Dic₆₇	—	4	1	no	—
387	C₂²×Dic₆₇	—	4	1	no	—
388	C₂²×Dic₆₇	—	4	1	no	—
389	C₂²×Dic₆₇	—	4	1	no	—
390	C₂²×Dic₆₇	—	4	1	no	—
391	C₂²×Dic₆₇	—	4	1	no	—
392	C₂²×Dic₆₇	—	4	1	no	—
393	C₂²×Dic₆₇	—	4	1	no	—
394	C₂²×Dic₆₇	—	4	1	no	—
395	C₂²×Dic₆₇	—	4	1	no	—
396	C₂²×Dic₆₇	—	4	1	no	—
397	C₂²×Dic₆₇	—	4	16	no	—
398	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₄⋊Dic₆₇	—	2	2	no	—
415	C₄⋊Dic₆₇	—	2	2	no	—
416	C₄⋊Dic₆₇	—	2	2	no	—
417	C₄⋊Dic₆₇	—	2	2	no	—
418	C₄⋊Dic₆₇	—	2	2	no	—
419	C₄⋊Dic₆₇	—	2	2	no	—
420	C₄⋊Dic₆₇	—	4	1	no	—
421	C₄⋊Dic₆₇	—	4	1	no	—
422	C₄⋊Dic₆₇	—	4	1	no	—
423	C₄⋊Dic₆₇	—	4	1	no	—
424	C₄⋊Dic₆₇	—	4	1	no	—
425	C₄⋊Dic₆₇	—	4	1	no	—
426	C₄⋊Dic₆₇	—	4	1	no	—
427	C₄⋊Dic₆₇	—	4	1	no	—
428	C₄⋊Dic₆₇	—	4	1	no	—
429	C₄⋊Dic₆₇	—	4	1	no	—
430	C₄⋊Dic₆₇	—	4	1	no	—
431	C₄⋊Dic₆₇	—	4	1	no	—
432	C₄⋊Dic₆₇	—	4	1	no	—
433	C₄⋊Dic₆₇	—	4	1	no	—
434	C₄⋊Dic₆₇	—	4	1	no	—
435	C₄⋊Dic₆₇	—	4	1	no	—
436	C₄⋊Dic₆₇	—	4	1	no	—
437	C₄⋊Dic₆₇	—	4	1	no	—
438	Dic₆₇⋊C₄	—	2	2	no	—
439	Dic₆₇⋊C₄	—	2	2	no	—
440	Dic₆₇⋊C₄	—	2	2	no	—
441	Dic₆₇⋊C₄	—	2	2	no	—
442	Dic₆₇⋊C₄	—	4	1	no	—
443	Dic₆₇⋊C₄	—	4	1	no	—
444	Dic₆₇⋊C₄	—	4	1	no	—
445	Dic₆₇⋊C₄	—	4	1	no	—
446	Dic₆₇⋊C₄	—	4	1	no	—
447	Dic₆₇⋊C₄	—	4	1	no	—
448	Dic₆₇⋊C₄	—	4	1	no	—
449	Dic₆₇⋊C₄	—	4	1	no	—
450	Dic₆₇⋊C₄	—	4	1	no	—
451	Dic₆₇⋊C₄	—	4	1	no	—
452	Dic₆₇⋊C₄	—	4	1	no	—
453	Dic₆₇⋊C₄	—	4	1	no	—
454	Dic₆₇⋊C₄	—	4	1	no	—
455	Dic₆₇⋊C₄	—	4	1	no	—
456	Dic₆₇⋊C₄	—	4	1	no	—
457	Dic₆₇⋊C₄	—	4	1	no	—
458	Dic₆₇⋊C₄	—	4	1	no	—
459	Dic₆₇⋊C₄	—	4	1	no	—
460	Dic₆₇⋊C₄	—	4	1	no	—
461	Dic₆₇⋊C₄	—	4	1	no	—
462	C₂²⋊Dic₆₇	—	2	2	no	—
463	C₂²⋊Dic₆₇	—	2	2	no	—
464	C₂²⋊Dic₆₇	—	2	2	no	—
465	C₂²⋊Dic₆₇	—	2	2	no	—
466	C₂²⋊Dic₆₇	—	4	1	no	—
467	C₂²⋊Dic₆₇	—	4	1	no	—
468	C₂²⋊Dic₆₇	—	4	1	no	—
469	C₂²⋊Dic₆₇	—	4	1	no	—
470	C₂²⋊Dic₆₇	—	4	1	no	—
471	C₂²⋊Dic₆₇	—	4	1	no	—
472	C₂²⋊Dic₆₇	—	4	1	no	—
473	C₂²⋊Dic₆₇	—	4	1	no	—
474	C₂²⋊Dic₆₇	—	4	1	no	—
475	C₂²⋊Dic₆₇	—	4	1	no	—
476	C₂²⋊Dic₆₇	—	4	1	no	—
477	C₂²⋊Dic₆₇	—	4	1	no	—
478	C₄×Dic₆₇	—	4	1	no	—
479	C₄×Dic₆₇	—	4	1	no	—
480	C₄×Dic₆₇	—	4	1	no	—
481	C₄×Dic₆₇	—	4	1	no	—
482	C₂⁴×C₆₇	—	2	2	no	—
483	C₂⁴×C₆₇	—	2	2	no	—
484	C₂⁴×C₆₇	—	4	1	no	—
485	C₂⁴×C₆₇	—	4	1	no	—
486	C₂⁴×C₆₇	—	4	1	no	—
487	C₂⁴×C₆₇	—	4	1	no	—
488	C₂⁴×C₆₇	C₂×Q₈	1	4	yes	—
489	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₆₇	—	4	1	no	—
493	C₂²×C₄×C₆₇	—	4	1	no	—
494	C₂²×C₄×C₆₇	—	4	1	no	—
495	C₂²×C₄×C₆₇	—	4	1	no	—
496	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
497	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
498	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
510	C₄⋊C₄×C₆₇	—	4	1	no	—
511	C₄⋊C₄×C₆₇	—	4	1	no	—
512	C₄⋊C₄×C₆₇	—	4	1	no	—
513	C₄⋊C₄×C₆₇	—	4	1	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	2	2	no	—
516	C₂²⋊C₄×C₆₇	—	2	2	no	—
517	C₂²⋊C₄×C₆₇	—	2	2	no	—
518	C₂²⋊C₄×C₆₇	—	4	1	no	—
519	C₂²⋊C₄×C₆₇	—	4	1	no	—
520	C₂²⋊C₄×C₆₇	—	4	1	no	—
521	C₂²⋊C₄×C₆₇	—	4	1	no	—
522	C₂²⋊C₄×C₆₇	—	4	1	no	—
523	C₂²⋊C₄×C₆₇	—	4	1	no	—
524	C₂²⋊C₄×C₆₇	—	4	1	no	—
525	C₂²⋊C₄×C₆₇	—	4	1	no	—
526	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
527	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
528	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
529	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
530	C₄²×C₆₇	—	4	1	no	—
531	C₄²×C₆₇	—	4	1	no	—
532	C₄²×C₆₇	—	4	1	no	—
533	C₄²×C₆₇	—	4	1	no	—
534	C₂³×C₆₇	—	2	1	no	—
535	C₂³×C₆₇	—	2	1	no	—
536	C₂³×C₆₇	—	2	1	no	—
537	C₂³×C₆₇	—	2	1	no	—
538	C₂³×C₆₇	—	2	8	no	—
539	C₂³×C₆₇	—	2	1	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	1	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	1	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	—	2	1	no	—
547	C₂³×C₆₇	—	2	1	no	—
548	C₂³×C₆₇	—	2	1	no	—
549	C₂³×C₆₇	—	2	1	no	—
550	C₂³×C₆₇	—	2	1	no	—
551	C₂³×C₆₇	—	4	4	no	—
552	C₂³×C₆₇	—	4	4	no	—
553	C₂³×C₆₇	—	4	4	no	—
554	C₂³×C₆₇	—	4	4	no	—
555	C₂³×C₆₇	—	4	4	no	—
556	C₂³×C₆₇	—	4	4	no	—
557	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
558	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
559	C₂³×C₆₇	C₂²×Q₈	1	2	yes	—
560	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
561	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
562	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
563	C₂×C₄×C₆₇	—	2	1	no	—
564	C₂×C₄×C₆₇	—	2	1	no	—
565	C₂×C₄×C₆₇	—	2	1	no	—
566	C₂×C₄×C₆₇	—	2	1	no	—
567	C₂×C₄×C₆₇	—	2	1	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	1	no	—
578	C₂×C₄×C₆₇	—	2	1	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	2	1	no	—
582	C₂×C₄×C₆₇	—	2	1	no	—
583	C₂×C₄×C₆₇	—	2	1	no	—
584	C₂×C₄×C₆₇	—	2	1	no	—
585	C₂×C₄×C₆₇	—	2	1	no	—
586	C₂×C₄×C₆₇	—	2	1	no	—
587	C₂×C₄×C₆₇	—	2	1	no	—
588	C₂×C₄×C₆₇	—	2	1	no	—
589	C₂×C₄×C₆₇	—	2	1	no	—
590	C₂×C₄×C₆₇	—	2	1	no	—
591	C₂×C₄×C₆₇	—	2	1	no	—
592	C₂×C₄×C₆₇	—	2	1	no	—
593	C₂×C₄×C₆₇	—	2	1	no	—
594	C₂×C₄×C₆₇	—	2	1	no	—
595	C₂×C₄×C₆₇	—	4	4	no	—
596	C₂×C₄×C₆₇	—	4	4	no	—
597	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
598	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
599	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
600	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
601	C₂×Dic₆₇	—	2	1	no	—
602	C₂×Dic₆₇	—	2	1	no	—
603	C₂×Dic₆₇	—	2	1	no	—
604	C₂×Dic₆₇	—	2	1	no	—
605	C₂×Dic₆₇	—	2	1	no	—
606	C₂×Dic₆₇	—	2	1	no	—
607	C₂×Dic₆₇	—	2	1	no	—
608	C₂×Dic₆₇	—	2	1	no	—
609	C₂×Dic₆₇	—	2	1	no	—
610	C₂×Dic₆₇	—	2	1	no	—
611	C₂×Dic₆₇	—	2	1	no	—
612	C₂×Dic₆₇	—	2	1	no	—
613	C₂×Dic₆₇	—	2	1	no	—
614	C₂×Dic₆₇	—	2	1	no	—
615	C₂×Dic₆₇	—	2	1	no	—
616	C₂×Dic₆₇	—	2	1	no	—
617	C₂×Dic₆₇	—	2	1	no	—
618	C₂×Dic₆₇	—	2	1	no	—
619	C₂×Dic₆₇	—	2	1	no	—
620	C₂×Dic₆₇	—	2	1	no	—
621	C₂×Dic₆₇	—	2	1	no	—
622	C₂×Dic₆₇	—	2	1	no	—
623	C₂×Dic₆₇	—	2	1	no	—
624	C₂×Dic₆₇	—	2	1	no	—
625	C₂×Dic₆₇	—	2	1	no	—
626	C₂×Dic₆₇	—	2	1	no	—
627	C₂×Dic₆₇	—	2	1	no	—
628	C₂×Dic₆₇	—	2	1	no	—
629	C₂×Dic₆₇	—	2	1	no	—
630	C₂×Dic₆₇	—	2	1	no	—
631	C₂×Dic₆₇	—	2	1	no	—
632	C₂×Dic₆₇	—	2	1	no	—
633	C₂×Dic₆₇	—	2	1	no	—
634	C₂×Dic₆₇	—	2	1	no	—
635	C₂×Dic₆₇	—	2	1	no	—
636	C₂×Dic₆₇	—	2	1	no	—
637	C₂×Dic₆₇	—	2	1	no	—
638	C₂×Dic₆₇	—	2	1	no	—
639	C₂×Dic₆₇	—	2	1	no	—
640	C₂×Dic₆₇	—	2	1	no	—
641	C₂×Dic₆₇	—	2	1	no	—
642	C₂×Dic₆₇	—	2	1	no	—
643	C₂×Dic₆₇	—	2	1	no	—
644	C₂×Dic₆₇	—	2	1	no	—
645	C₂×Dic₆₇	—	2	1	no	—
646	C₂×Dic₆₇	—	2	1	no	—
647	C₂×Dic₆₇	—	4	4	no	—
648	C₂×Dic₆₇	—	4	4	no	—
649	C₂×Dic₆₇	—	4	4	no	—
650	C₂×Dic₆₇	—	4	4	no	—
651	C₂×Dic₆₇	—	4	4	no	—
652	C₂×Dic₆₇	—	4	4	no	—
653	C₂×Dic₆₇	—	8	2	no	—
654	C₂×Dic₆₇	—	8	2	no	—
655	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
656	C₂×Dic₆₇	H(5,𝔽₂)	1	2	yes	—
657	Dic₁₃₄	—	8	2	no	—
658	Dic₁₃₄	—	8	2	no	—
659	Dic₁₃₄	—	8	2	no	—
660	Dic₁₃₄	—	8	2	no	—
661	C₂²×C₆₇	—	2	2	no	—
662	C₂²×C₆₇	—	2	2	no	—
663	C₂²×C₆₇	—	2	2	no	—
664	C₂²×C₆₇	—	2	2	no	—
665	C₂²×C₆₇	—	2	2	no	—
666	C₂²×C₆₇	—	2	2	no	—
667	C₂²×C₆₇	—	2	2	no	—
668	C₂²×C₆₇	—	2	2	no	—
669	C₂²×C₆₇	—	2	2	no	—
670	C₂²×C₆₇	—	2	2	no	—
671	C₂²×C₆₇	—	2	2	no	—
672	C₂²×C₆₇	—	2	2	no	—
673	C₂²×C₆₇	—	4	16	no	—
674	C₂²×C₆₇	—	4	1	no	—
675	C₂²×C₆₇	—	4	1	no	—
676	C₂²×C₆₇	—	4	1	no	—
677	C₂²×C₆₇	—	4	1	no	—
678	C₂²×C₆₇	—	4	1	no	—
679	C₂²×C₆₇	—	4	1	no	—
680	C₂²×C₆₇	—	4	1	no	—
681	C₂²×C₆₇	—	4	1	no	—
682	C₂²×C₆₇	#544	1	4	yes	—
683	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
684	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
688	C₂²×C₆₇	#585	1	1	yes	characteristic
689	C₂²×C₆₇	#585	1	1	yes	characteristic
690	C₄×C₆₇	—	2	2	no	—
691	C₄×C₆₇	—	2	2	no	—
692	C₄×C₆₇	—	2	2	no	—
693	C₄×C₆₇	—	2	2	no	—
694	C₄×C₆₇	—	4	1	no	—
695	C₄×C₆₇	—	4	1	no	—
696	C₄×C₆₇	—	4	1	no	—
697	C₄×C₆₇	—	4	1	no	—
698	C₄×C₆₇	—	4	1	no	—
699	C₄×C₆₇	—	4	1	no	—
700	C₄×C₆₇	—	4	1	no	—
701	C₄×C₆₇	—	4	1	no	—
702	Dic₆₇	—	2	2	no	—
703	Dic₆₇	—	2	2	no	—
704	Dic₆₇	—	4	1	no	—
705	Dic₆₇	—	4	1	no	—
706	Dic₆₇	—	4	1	no	—
707	Dic₆₇	—	4	1	no	—
708	Dic₆₇	—	4	1	no	—
709	Dic₆₇	—	4	1	no	—
710	Dic₆₇	—	4	1	no	—
711	Dic₆₇	—	4	1	no	—
712	Dic₆₇	—	4	1	no	—
713	Dic₆₇	—	4	1	no	—
714	Dic₆₇	—	4	1	no	—
715	Dic₆₇	—	4	1	no	—
716	Dic₆₇	—	4	1	no	—
717	Dic₆₇	—	4	1	no	—
718	#36748	—	67	1	no	maximal, Sylow
719	C₂×C₆₇	—	2	4	no	—
720	C₂×C₆₇	—	4	2	no	—
721	C₂×C₆₇	—	4	2	no	—
722	C₂×C₆₇	C₂×#544	1	1	yes	characteristic
723	C₂×C₆₇	#3501	1	1	yes	characteristic
724	C₂×C₆₇	#3501	1	1	yes	characteristic
725	C₂×C₆₇	#3532	1	1	yes	characteristic
726	C₂×C₆₇	#3533	1	1	yes	characteristic
727	C₂×C₆₇	#3541	1	1	yes	characteristic
728	C₂×C₆₇	#3541	1	1	yes	characteristic
729	#2848	—	67	1	no	—
730	#2848	—	67	1	no	—
731	#2807	—	67	1	no	—
732	#2790	—	67	1	no	—
733	#2790	—	67	1	no	—
734	#2788	—	67	1	no	—
735	#2788	—	67	1	no	—
736	#2768	—	67	1	no	—
737	#2768	—	67	1	no	—
738	#2763	—	67	1	no	—
739	#2742	—	67	1	no	—
740	#2729	—	67	1	no	—
741	#2729	—	67	1	no	—
742	#2720	—	67	1	no	—
743	#2720	—	67	1	no	—
744	#2704	—	67	1	no	—
745	#2704	—	67	1	no	—
746	#2677	—	67	1	no	—
747	#2626	—	67	1	no	—
748	#2626	—	67	1	no	—
749	#2569	—	67	1	no	—
750	#2569	—	67	1	no	—
751	#2549	—	67	1	no	—
752	#2549	—	67	1	no	—
753	#2442	—	67	1	no	—
754	#2442	—	67	1	no	—
755	#2440	—	67	1	no	—
756	#2440	—	67	1	no	—
757	#2312	—	67	1	no	—
758	#2312	D₆₇	1	1	yes	characteristic
759	C₂×#385	—	67	1	no	—
760	C₆₇	#36748	1	1	yes	characteristic, complemented, Sylow
761	C₂⁴×C₄	—	67	1	no	—
762	C₂×C₄⋊Q₈	—	67	1	no	—
763	C₂×C₄⋊Q₈	—	67	1	no	—
764	C₂×#125	—	67	1	no	—
765	C₂×#125	—	67	1	no	—
766	C₂×C₂²⋊Q₈	—	67	1	no	—
767	C₂×C₂²⋊Q₈	—	67	1	no	—
768	C₂×C₂²⋊Q₈	—	67	1	no	—
769	C₂×C₂²⋊Q₈	—	67	1	no	—
770	C₂×C₂²⋊Q₈	—	67	1	no	—
771	C₂×C₂²⋊Q₈	—	67	1	no	—
772	C₂×C₂²⋊Q₈	—	67	1	no	—
773	C₂×C₂²⋊Q₈	—	67	1	no	—
774	C₂²×C₄⋊C₄	—	67	1	no	—
775	C₂²×C₄⋊C₄	—	67	1	no	—
776	C₂²×C₂²⋊C₄	—	67	1	no	—
777	C₂²×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
778	#400	—	67	1	no	—
779	#400	—	67	1	no	—
780	#400	—	67	1	no	—
781	#400	—	67	1	no	—
782	#400	—	67	1	no	—
783	#400	—	67	1	no	—
784	#400	—	67	1	no	—
785	#400	—	67	1	no	—
786	#399	—	67	1	no	—
787	#399	—	67	1	no	—
788	#399	—	67	1	no	—
789	#399	—	67	1	no	—
790	#398	—	67	1	no	—
791	#398	—	67	1	no	—
792	#398	—	67	1	no	—
793	#398	—	67	1	no	—
794	#398	—	67	1	no	—
795	#398	—	67	1	no	—
796	#398	—	67	1	no	—
797	#398	—	67	1	no	—
798	#398	—	67	1	no	—
799	#398	—	67	1	no	—
800	#398	—	67	1	no	—
801	#398	—	67	1	no	—
802	#398	—	67	1	no	—
803	#398	—	67	1	no	—
804	#398	—	67	1	no	—
805	#398	—	67	1	no	—
806	#396	—	67	1	no	—
807	#396	—	67	1	no	—
808	#396	—	67	1	no	—
809	#396	—	67	1	no	—
810	#396	—	67	1	no	—
811	#396	—	67	1	no	—
812	#396	—	67	1	no	—
813	#396	—	67	1	no	—
814	#395	—	67	1	no	—
815	#395	—	67	1	no	—
816	#395	—	67	1	no	—
817	#395	—	67	1	no	—
818	#395	—	67	1	no	—
819	#395	—	67	1	no	—
820	#395	—	67	1	no	—
821	#395	—	67	1	no	—
822	#393	—	67	1	no	—
823	#393	—	67	1	no	—
824	#393	—	67	1	no	—
825	#393	—	67	1	no	—
826	#391	—	67	1	no	—
827	#391	—	67	1	no	—
828	#391	—	67	1	no	—
829	#391	—	67	1	no	—
830	#389	—	67	1	no	—
831	#389	—	67	1	no	—
832	#389	—	67	1	no	—
833	#389	—	67	1	no	—
834	#389	—	67	1	no	—
835	#389	—	67	1	no	—
836	#389	—	67	1	no	—
837	#389	—	67	1	no	—
838	#389	—	67	1	no	—
839	#389	—	67	1	no	—
840	#389	—	67	1	no	—
841	#389	—	67	1	no	—
842	#388	—	67	1	no	—
843	#388	—	67	1	no	—
844	#388	—	67	1	no	—
845	#388	—	67	1	no	—
846	#388	—	67	1	no	—
847	#388	—	67	1	no	—
848	#388	—	67	1	no	—
849	#388	—	67	1	no	—
850	#388	C₂×D₆₇	1	1	yes	characteristic
851	#388	C₂×D₆₇	1	1	yes	characteristic
852	#388	C₂×D₆₇	1	1	yes	characteristic
853	#388	C₂×D₆₇	1	1	yes	characteristic
854	#388	C₂×D₆₇	1	1	yes	characteristic
855	#388	C₂×D₆₇	1	1	yes	characteristic
856	#388	C₂×D₆₇	1	1	yes	characteristic
857	#388	C₂×D₆₇	1	1	yes	characteristic
858	#387	—	67	1	no	—
859	#387	—	67	1	no	—
860	#387	—	67	1	no	—
861	#387	—	67	1	no	—
862	#387	—	67	1	no	—
863	#387	—	67	1	no	—
864	#387	—	67	1	no	—
865	#387	—	67	1	no	—
866	#385	—	67	1	no	—
867	#385	—	67	1	no	—
868	#385	—	67	1	no	—
869	#385	—	67	1	no	—
870	#385	—	67	1	no	—
871	#385	—	67	1	no	—
872	#385	—	67	1	no	—
873	#385	—	67	1	no	—
874	#385	—	67	1	no	—
875	#385	—	67	1	no	—
876	#385	—	67	1	no	—
877	#385	—	67	1	no	—
878	#385	—	67	1	no	—
879	#385	—	67	1	no	—
880	#385	—	67	1	no	—
881	#385	—	67	1	no	—
882	#385	—	67	1	no	—
883	#385	—	67	1	no	—
884	#385	—	67	1	no	—
885	#385	—	67	1	no	—
886	#385	—	67	1	no	—
887	#385	—	67	1	no	—
888	#385	—	67	1	no	—
889	#385	—	67	1	no	—
890	#384	—	67	1	no	—
891	#384	—	67	1	no	—
892	#382	—	67	1	no	—
893	#382	—	67	1	no	—
894	#380	—	67	1	no	—
895	#380	—	67	1	no	—
896	#380	—	67	1	no	—
897	#380	—	67	1	no	—
898	#380	—	67	1	no	—
899	#380	—	67	1	no	—
900	#380	—	67	1	no	—
901	#380	—	67	1	no	—
902	#380	—	67	1	no	—
903	#380	—	67	1	no	—
904	#380	C₂×D₆₇	1	1	yes	characteristic
905	#380	C₂×D₆₇	1	1	yes	characteristic
906	#379	—	67	1	no	—
907	#379	—	67	1	no	—
908	#379	C₂×D₆₇	1	1	yes	characteristic
909	#379	C₂×D₆₇	1	1	yes	characteristic
910	C₄×C₂²⋊C₄	—	67	1	no	—
911	C₄×C₂²⋊C₄	—	67	1	no	—
912	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
913	C₄×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic
914	C₂×#95	—	67	1	no	—
915	C₂×#95	—	67	1	no	—
916	C₂⁵	C₂²×D₆₇	1	1	yes	characteristic
917	C₂²×Q₈	—	67	1	no	—
918	C₂²×Q₈	—	67	1	no	—
919	C₂²×Q₈	—	67	1	no	—
920	C₂²×Q₈	—	67	1	no	—
921	C₂³×C₄	—	268	2	no	—
922	C₂³×C₄	—	268	2	no	—
923	C₂³×C₄	—	268	2	no	—
924	C₂³×C₄	—	67	1	no	—
925	C₂³×C₄	—	67	1	no	—
926	C₂³×C₄	—	67	1	no	—
927	C₂³×C₄	—	67	1	no	—
928	C₂³×C₄	—	67	1	no	—
929	C₂³×C₄	—	67	1	no	—
930	C₂³×C₄	—	67	1	no	—
931	C₂³×C₄	—	67	1	no	—
932	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
933	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
934	C₄⋊Q₈	—	268	2	no	—
935	C₄⋊Q₈	—	268	2	no	—
936	#125	—	268	2	no	—
937	#125	—	268	2	no	—
938	C₂²⋊Q₈	—	268	2	no	—
939	C₂²⋊Q₈	—	268	2	no	—
940	C₂²⋊Q₈	—	268	2	no	—
941	C₂²⋊Q₈	—	268	2	no	—
942	C₂²⋊Q₈	—	268	2	no	—
943	C₂²⋊Q₈	—	268	2	no	—
944	C₂²⋊Q₈	—	268	2	no	—
945	C₂²⋊Q₈	—	268	2	no	—
946	C₂×C₄⋊C₄	—	268	2	no	—
947	C₂×C₄⋊C₄	—	268	2	no	—
948	C₂×C₄⋊C₄	—	67	1	no	—
949	C₂×C₄⋊C₄	—	67	1	no	—
950	C₂×C₄⋊C₄	—	67	1	no	—
951	C₂×C₄⋊C₄	—	67	1	no	—
952	C₂×C₄⋊C₄	—	67	1	no	—
953	C₂×C₄⋊C₄	—	67	1	no	—
954	C₂×C₄⋊C₄	—	67	1	no	—
955	C₂×C₄⋊C₄	—	67	1	no	—
956	C₂×C₄⋊C₄	—	67	1	no	—
957	C₂×C₄⋊C₄	—	67	1	no	—
958	C₂×C₄⋊C₄	—	67	1	no	—
959	C₂×C₄⋊C₄	—	67	1	no	—
960	C₂×C₄⋊C₄	—	67	1	no	—
961	C₂×C₄⋊C₄	—	67	1	no	—
962	C₂×C₄⋊C₄	—	67	1	no	—
963	C₂×C₄⋊C₄	—	67	1	no	—
964	C₂×C₄⋊C₄	—	67	1	no	—
965	C₂×C₄⋊C₄	—	67	1	no	—
966	C₂×C₄⋊C₄	—	67	1	no	—
967	C₂×C₄⋊C₄	—	67	1	no	—
968	C₂×C₄⋊C₄	—	67	1	no	—
969	C₂×C₄⋊C₄	—	67	1	no	—
970	C₂×C₄⋊C₄	—	67	1	no	—
971	C₂×C₄⋊C₄	—	67	1	no	—
972	C₂×C₄⋊C₄	—	67	1	no	—
973	C₂×C₄⋊C₄	—	67	1	no	—
974	C₂×C₄⋊C₄	—	67	1	no	—
975	C₂×C₄⋊C₄	—	67	1	no	—
976	C₂×C₄⋊C₄	—	67	1	no	—
977	C₂×C₄⋊C₄	—	67	1	no	—
978	C₂×C₄⋊C₄	—	67	1	no	—
979	C₂×C₄⋊C₄	—	67	1	no	—
980	C₂×C₄⋊C₄	—	67	1	no	—
981	C₂×C₄⋊C₄	—	67	1	no	—
982	C₂×C₄⋊C₄	—	67	1	no	—
983	C₂×C₄⋊C₄	—	67	1	no	—
984	C₂×C₄⋊C₄	—	67	1	no	—
985	C₂×C₄⋊C₄	—	67	1	no	—
986	C₂×C₄⋊C₄	—	67	1	no	—
987	C₂×C₄⋊C₄	—	67	1	no	—
988	C₂×C₄⋊C₄	—	67	1	no	—
989	C₂×C₄⋊C₄	—	67	1	no	—
990	C₂×C₄⋊C₄	—	67	1	no	—
991	C₂×C₄⋊C₄	—	67	1	no	—
992	C₂×C₄⋊C₄	—	67	1	no	—
993	C₂×C₄⋊C₄	—	67	1	no	—
994	C₂×C₄⋊C₄	—	67	1	no	—
995	C₂×C₄⋊C₄	—	67	1	no	—
996	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	—	268	2	no	—
1001	C₂×C₂²⋊C₄	—	67	1	no	—
1002	C₂×C₂²⋊C₄	—	67	1	no	—
1003	C₂×C₂²⋊C₄	—	67	1	no	—
1004	C₂×C₂²⋊C₄	—	67	1	no	—
1005	C₂×C₂²⋊C₄	—	67	1	no	—
1006	C₂×C₂²⋊C₄	—	67	1	no	—
1007	C₂×C₂²⋊C₄	—	67	1	no	—
1008	C₂×C₂²⋊C₄	—	67	1	no	—
1009	C₂×C₂²⋊C₄	—	67	1	no	—
1010	C₂×C₂²⋊C₄	—	67	1	no	—
1011	C₂×C₂²⋊C₄	—	67	1	no	—
1012	C₂×C₂²⋊C₄	—	67	1	no	—
1013	C₂×C₂²⋊C₄	—	67	1	no	—
1014	C₂×C₂²⋊C₄	—	67	1	no	—
1015	C₂×C₂²⋊C₄	—	67	1	no	—
1016	C₂×C₂²⋊C₄	—	67	1	no	—
1017	C₂×C₂²⋊C₄	Dic₁₃₄	1	8	yes	complemented
1018	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
1034	C₂×C₄²	—	67	1	no	—
1035	C₂×C₄²	—	67	1	no	—
1036	C₂×C₄²	—	67	1	no	—
1037	C₂×C₄²	—	67	1	no	—
1038	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1039	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1040	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1041	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1042	#95	—	67	1	no	—
1043	#95	—	67	1	no	—
1044	#95	—	67	1	no	—
1045	#95	—	67	1	no	—
1046	#95	—	67	1	no	—
1047	#95	—	67	1	no	—
1048	#95	—	67	1	no	—
1049	#95	—	67	1	no	—
1050	#95	—	67	1	no	—
1051	#95	—	67	1	no	—
1052	#95	—	67	1	no	—
1053	#95	—	67	1	no	—
1054	#95	—	67	1	no	—
1055	#95	—	67	1	no	—
1056	#95	—	67	1	no	—
1057	#95	—	67	1	no	—
1058	#95	—	67	1	no	—
1059	#95	—	67	1	no	—
1060	#95	—	67	1	no	—
1061	#95	—	67	1	no	—
1062	#95	—	67	1	no	—
1063	#95	—	67	1	no	—
1064	#95	—	67	1	no	—
1065	#95	—	67	1	no	—
1066	#95	—	67	1	no	—
1067	#95	—	67	1	no	—
1068	#95	—	67	1	no	—
1069	#95	—	67	1	no	—
1070	#95	—	67	1	no	—
1071	#95	—	67	1	no	—
1072	#95	—	67	1	no	—
1073	#95	—	67	1	no	—
1074	#95	—	67	1	no	—
1075	#95	—	67	1	no	—
1076	#95	—	67	1	no	—
1077	#95	—	67	1	no	—
1078	#95	—	67	1	no	—
1079	#95	—	67	1	no	—
1080	#95	—	67	1	no	—
1081	#95	—	67	1	no	—
1082	#95	C₂²×D₆₇	1	1	yes	characteristic
1083	#95	C₂²×D₆₇	1	1	yes	characteristic
1084	#95	C₂²×D₆₇	1	1	yes	characteristic
1085	#95	C₂²×D₆₇	1	1	yes	characteristic
1086	#95	C₂²×D₆₇	1	1	yes	characteristic
1087	#95	C₂²×D₆₇	1	1	yes	characteristic
1088	#95	C₂²×D₆₇	1	1	yes	characteristic
1089	#95	C₂²×D₆₇	1	1	yes	characteristic
1090	C₂⁴	—	2	2	no	—
1091	C₂⁴	—	2	2	no	—
1092	C₂⁴	—	4	1	no	—
1093	C₂⁴	—	4	1	no	—
1094	C₂⁴	—	4	1	no	—
1095	C₂⁴	—	4	1	no	—
1096	C₂⁴	C₂×Dic₁₃₄	1	4	yes	—
1097	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1098	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1099	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1100	C₂×Q₈	—	268	1	no	—
1101	C₂×Q₈	—	268	1	no	—
1102	C₂×Q₈	—	268	1	no	—
1103	C₂×Q₈	—	268	1	no	—
1104	C₂×Q₈	—	268	1	no	—
1105	C₂×Q₈	—	268	1	no	—
1106	C₂×Q₈	—	268	1	no	—
1107	C₂×Q₈	—	268	1	no	—
1108	C₂×Q₈	—	268	1	no	—
1109	C₂×Q₈	—	268	1	no	—
1110	C₂×Q₈	—	134	2	no	—
1111	C₂×Q₈	—	134	2	no	—
1112	C₂²×C₄	—	4	1	no	—
1113	C₂²×C₄	—	4	1	no	—
1114	C₂²×C₄	—	4	1	no	—
1115	C₂²×C₄	—	4	1	no	—
1116	C₂²×C₄	—	268	16	no	—
1117	C₂²×C₄	—	268	1	no	—
1118	C₂²×C₄	—	268	1	no	—
1119	C₂²×C₄	—	268	1	no	—
1120	C₂²×C₄	—	268	1	no	—
1121	C₂²×C₄	—	268	1	no	—
1122	C₂²×C₄	—	268	1	no	—
1123	C₂²×C₄	—	268	1	no	—
1124	C₂²×C₄	—	268	1	no	—
1125	C₂²×C₄	—	268	1	no	—
1126	C₂²×C₄	—	268	1	no	—
1127	C₂²×C₄	—	268	1	no	—
1128	C₂²×C₄	—	268	1	no	—
1129	C₂²×C₄	—	268	1	no	—
1130	C₂²×C₄	—	268	1	no	—
1131	C₂²×C₄	—	67	1	no	—
1132	C₂²×C₄	—	67	1	no	—
1133	C₂²×C₄	—	67	1	no	—
1134	C₂²×C₄	—	67	1	no	—
1135	C₂²×C₄	—	67	1	no	—
1136	C₂²×C₄	—	67	1	no	—
1137	C₂²×C₄	—	67	1	no	—
1138	C₂²×C₄	—	67	1	no	—
1139	C₂²×C₄	—	67	1	no	—
1140	C₂²×C₄	—	67	1	no	—
1141	C₂²×C₄	—	67	1	no	—
1142	C₂²×C₄	—	67	1	no	—
1143	C₂²×C₄	—	67	1	no	—
1144	C₂²×C₄	—	67	1	no	—
1145	C₂²×C₄	—	67	1	no	—
1146	C₂²×C₄	—	67	1	no	—
1147	C₂²×C₄	—	134	2	no	—
1148	C₂²×C₄	—	134	2	no	—
1149	C₂²×C₄	—	134	2	no	—
1150	C₂²×C₄	—	134	2	no	—
1151	C₂²×C₄	—	134	2	no	—
1152	C₂²×C₄	—	134	2	no	—
1153	C₂²×C₄	—	134	2	no	—
1154	C₂²×C₄	—	134	2	no	—
1155	C₂²×C₄	—	134	2	no	—
1156	C₂²×C₄	—	134	2	no	—
1157	C₂²×C₄	C₂×Dic₁₃₄	1	4	yes	—
1158	C₂²×C₄	C₂×Dic₁₃₄	1	4	yes	—
1159	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1162	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1163	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1164	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1165	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1166	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1167	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1170	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	—	4	1	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	4	1	no	—
1175	C₄⋊C₄	—	268	1	no	—
1176	C₄⋊C₄	—	268	1	no	—
1177	C₄⋊C₄	—	268	1	no	—
1178	C₄⋊C₄	—	268	1	no	—
1179	C₄⋊C₄	—	268	1	no	—
1180	C₄⋊C₄	—	268	1	no	—
1181	C₄⋊C₄	—	268	1	no	—
1182	C₄⋊C₄	—	268	1	no	—
1183	C₄⋊C₄	—	268	1	no	—
1184	C₄⋊C₄	—	268	1	no	—
1185	C₄⋊C₄	—	268	1	no	—
1186	C₄⋊C₄	—	268	1	no	—
1187	C₄⋊C₄	—	268	1	no	—
1188	C₄⋊C₄	—	268	1	no	—
1189	C₄⋊C₄	—	268	1	no	—
1190	C₄⋊C₄	—	268	1	no	—
1191	C₄⋊C₄	—	268	1	no	—
1192	C₄⋊C₄	—	268	1	no	—
1193	C₄⋊C₄	—	268	1	no	—
1194	C₄⋊C₄	—	268	1	no	—
1195	C₄⋊C₄	—	268	1	no	—
1196	C₄⋊C₄	—	268	1	no	—
1197	C₄⋊C₄	—	268	1	no	—
1198	C₄⋊C₄	—	268	1	no	—
1199	C₄⋊C₄	—	268	1	no	—
1200	C₄⋊C₄	—	268	1	no	—
1201	C₄⋊C₄	—	268	1	no	—
1202	C₄⋊C₄	—	268	1	no	—
1203	C₄⋊C₄	—	268	1	no	—
1204	C₄⋊C₄	—	268	1	no	—
1205	C₄⋊C₄	—	268	1	no	—
1206	C₄⋊C₄	—	268	1	no	—
1207	C₄⋊C₄	—	268	1	no	—
1208	C₄⋊C₄	—	268	1	no	—
1209	C₄⋊C₄	—	268	1	no	—
1210	C₄⋊C₄	—	268	1	no	—
1211	C₄⋊C₄	—	268	1	no	—
1212	C₄⋊C₄	—	268	1	no	—
1213	C₄⋊C₄	—	134	2	no	—
1214	C₄⋊C₄	—	134	2	no	—
1215	C₄⋊C₄	—	134	2	no	—
1216	C₄⋊C₄	—	134	2	no	—
1217	C₄⋊C₄	—	134	2	no	—
1218	C₄⋊C₄	—	134	2	no	—
1219	C₄⋊C₄	—	134	2	no	—
1220	C₄⋊C₄	—	134	2	no	—
1221	C₄⋊C₄	—	134	2	no	—
1222	C₄⋊C₄	—	134	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	2	2	no	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	4	1	no	—
1228	C₂²⋊C₄	—	4	1	no	—
1229	C₂²⋊C₄	—	4	1	no	—
1230	C₂²⋊C₄	—	4	1	no	—
1231	C₂²⋊C₄	—	4	1	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	4	1	no	—
1235	C₂²⋊C₄	—	268	1	no	—
1236	C₂²⋊C₄	—	268	1	no	—
1237	C₂²⋊C₄	—	268	1	no	—
1238	C₂²⋊C₄	—	268	1	no	—
1239	C₂²⋊C₄	—	268	1	no	—
1240	C₂²⋊C₄	—	268	1	no	—
1241	C₂²⋊C₄	—	268	1	no	—
1242	C₂²⋊C₄	—	268	1	no	—
1243	C₂²⋊C₄	—	268	1	no	—
1244	C₂²⋊C₄	—	268	1	no	—
1245	C₂²⋊C₄	—	268	1	no	—
1246	C₂²⋊C₄	—	268	1	no	—
1247	C₂²⋊C₄	—	134	2	no	—
1248	C₂²⋊C₄	—	134	2	no	—
1249	C₂²⋊C₄	—	134	2	no	—
1250	C₂²⋊C₄	—	134	2	no	—
1251	C₂²⋊C₄	C₂×Dic₁₃₄	1	4	yes	—
1252	C₂²⋊C₄	C₂×Dic₁₃₄	1	4	yes	—
1253	C₂²⋊C₄	C₂×Dic₁₃₄	1	4	yes	—
1254	C₂²⋊C₄	C₂×Dic₁₃₄	1	4	yes	—
1255	C₄²	—	4	1	no	—
1256	C₄²	—	4	1	no	—
1257	C₄²	—	4	1	no	—
1258	C₄²	—	4	1	no	—
1259	C₄²	—	268	1	no	—
1260	C₄²	—	268	1	no	—
1261	C₄²	—	268	1	no	—
1262	C₄²	—	268	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	2	8	no	—
1268	C₂³	—	2	1	no	—
1269	C₂³	—	2	1	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	1	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	2	1	no	—
1275	C₂³	—	2	1	no	—
1276	C₂³	—	2	1	no	—
1277	C₂³	—	2	1	no	—
1278	C₂³	—	2	1	no	—
1279	C₂³	—	2	1	no	—
1280	C₂³	—	4	4	no	—
1281	C₂³	—	4	4	no	—
1282	C₂³	—	4	4	no	—
1283	C₂³	—	4	4	no	—
1284	C₂³	—	4	4	no	—
1285	C₂³	—	4	4	no	—
1286	C₂³	C₂²×Dic₁₃₄	1	2	yes	—
1287	C₂³	C₂²×Dic₁₃₄	1	2	yes	—
1288	C₂³	C₂²×Dic₁₃₄	1	2	yes	—
1289	C₂³	#14524089	1	2	yes	—
1290	C₂³	#14524090	1	2	yes	—
1291	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1292	Q₈	—	536	2	no	—
1293	Q₈	—	536	2	no	—
1294	Q₈	—	536	2	no	—
1295	Q₈	—	536	2	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	4	4	no	—
1329	C₂×C₄	—	4	4	no	—
1330	C₂×C₄	—	268	4	no	—
1331	C₂×C₄	—	268	4	no	—
1332	C₂×C₄	—	268	4	no	—
1333	C₂×C₄	—	268	4	no	—
1334	C₂×C₄	—	268	4	no	—
1335	C₂×C₄	—	268	4	no	—
1336	C₂×C₄	—	536	2	no	—
1337	C₂×C₄	—	536	2	no	—
1338	C₂×C₄	—	67	2	no	—
1339	C₂×C₄	—	67	2	no	—
1340	C₂×C₄	—	134	1	no	—
1341	C₂×C₄	—	134	1	no	—
1342	C₂×C₄	—	134	1	no	—
1343	C₂×C₄	—	134	1	no	—
1344	C₂×C₄	—	134	1	no	—
1345	C₂×C₄	—	134	1	no	—
1346	C₂×C₄	—	134	1	no	—
1347	C₂×C₄	—	134	1	no	—
1348	C₂×C₄	—	134	1	no	—
1349	C₂×C₄	—	134	1	no	—
1350	C₂×C₄	—	134	1	no	—
1351	C₂×C₄	—	134	1	no	—
1352	C₂×C₄	—	134	1	no	—
1353	C₂×C₄	—	134	1	no	—
1354	C₂×C₄	—	134	1	no	—
1355	C₂×C₄	—	134	1	no	—
1356	C₂×C₄	—	134	1	no	—
1357	C₂×C₄	—	134	1	no	—
1358	C₂×C₄	—	134	1	no	—
1359	C₂×C₄	—	134	1	no	—
1360	C₂×C₄	—	134	1	no	—
1361	C₂×C₄	—	134	1	no	—
1362	C₂×C₄	—	134	1	no	—
1363	C₂×C₄	—	134	1	no	—
1364	C₂×C₄	—	134	1	no	—
1365	C₂×C₄	—	134	1	no	—
1366	C₂×C₄	—	134	1	no	—
1367	C₂×C₄	—	134	1	no	—
1368	C₂×C₄	—	134	1	no	—
1369	C₂×C₄	—	134	1	no	—
1370	C₂×C₄	—	134	1	no	—
1371	C₂×C₄	—	134	1	no	—
1372	C₂×C₄	—	134	1	no	—
1373	C₂×C₄	—	134	1	no	—
1374	C₂×C₄	—	134	1	no	—
1375	C₂×C₄	—	134	1	no	—
1376	C₂×C₄	—	134	1	no	—
1377	C₂×C₄	—	134	1	no	—
1378	C₂×C₄	—	134	1	no	—
1379	C₂×C₄	—	134	1	no	—
1380	C₂×C₄	—	134	1	no	—
1381	C₂×C₄	—	134	1	no	—
1382	C₂×C₄	—	134	1	no	—
1383	C₂×C₄	—	134	1	no	—
1384	C₂×C₄	—	134	1	no	—
1385	C₂×C₄	—	134	1	no	—
1386	C₂×C₄	C₂²×Dic₁₃₄	1	2	yes	—
1387	C₂×C₄	C₂²×Dic₁₃₄	1	2	yes	—
1388	C₂×C₄	C₂²×Dic₁₃₄	1	2	yes	—
1389	C₂×C₄	C₂²×Dic₁₃₄	1	2	yes	—
1390	C₂²	—	2	2	no	—
1391	C₂²	—	2	2	no	—
1392	C₂²	—	2	2	no	—
1393	C₂²	—	2	2	no	—
1394	C₂²	—	2	2	no	—
1395	C₂²	—	2	2	no	—
1396	C₂²	—	2	2	no	—
1397	C₂²	—	2	2	no	—
1398	C₂²	—	2	2	no	—
1399	C₂²	—	2	2	no	—
1400	C₂²	—	2	2	no	—
1401	C₂²	—	2	2	no	—
1402	C₂²	—	4	16	no	—
1403	C₂²	—	4	1	no	—
1404	C₂²	—	4	1	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	1	no	—
1407	C₂²	—	4	1	no	—
1408	C₂²	—	4	1	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	#16864024	1	4	yes	—
1412	C₂²	C₂³×Dic₁₃₄	1	1	yes	characteristic
1413	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1414	C₂²	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1415	C₂²	C₂×#14524089	1	1	yes	characteristic
1416	C₂²	C₂×#14524090	1	1	yes	characteristic
1417	C₂²	#16864231	1	1	yes	characteristic
1418	C₂²	#16864231	1	1	yes	characteristic
1419	C₄	—	2	2	no	—
1420	C₄	—	2	2	no	—
1421	C₄	—	2	2	no	—
1422	C₄	—	2	2	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	1	no	—
1431	C₄	—	268	1	no	—
1432	C₄	—	268	1	no	—
1433	C₄	—	268	1	no	—
1434	C₄	—	268	1	no	—
1435	C₄	—	268	1	no	—
1436	C₄	—	268	1	no	—
1437	C₄	—	268	1	no	—
1438	C₄	—	268	1	no	—
1439	C₄	—	268	1	no	—
1440	C₄	—	268	1	no	—
1441	C₄	—	268	1	no	—
1442	C₄	—	268	1	no	—
1443	C₄	—	268	1	no	—
1444	C₄	—	268	1	no	—
1445	C₄	—	134	2	no	—
1446	C₄	—	134	2	no	—
1447	C₂	—	2	4	no	—
1448	C₂	—	4	2	no	—
1449	C₂	—	4	2	no	—
1450	C₂	C₂×#16864024	1	1	yes	characteristic
1451	C₂	#22574007	1	1	yes	characteristic
1452	C₂	#22574007	1	1	yes	characteristic
1453	C₂	#22574360	1	1	yes	characteristic
1454	C₂	#22574377	1	1	yes	characteristic
1455	C₂	#22574489	1	1	yes	characteristic
1456	C₂	#22574497	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₆₇
commutator, socle, cosocle	C₂³×C₆₇	C₂⁵
Fitting	C₆₇×#2312	C₂
prime radical	C₂⁵×C₆₇	C₂³
hypercenter	#2312	D₆₇
hypocenter	C₆₇	#36748
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ #2312

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #22568176	C₂	semidirect
4. #22567979	C₂	semidirect
5. #22567974	C₂	semidirect
6. #22567956	C₂	semidirect
7. #22567952	C₂	semidirect
8. #22567693	C₂	semidirect
9. #22567690	C₂	semidirect
10. #22567625	C₂	semidirect
11. #22567335	C₂	semidirect
12. #22567192	C₂	semidirect
13. #22567188	C₂	semidirect
14. #22567093	C₂	semidirect
15. #22567086	C₂	semidirect
16. #22566868	C₂	semidirect
17. #22566864	C₂	semidirect
18. #22566521	C₂	semidirect
21. #22565434	C₂	semidirect
22. #22565428	C₂	semidirect
23. #22565221	C₂	semidirect
24. #22565215	C₂	semidirect
25. #22563934	C₂	semidirect
26. #22563933	C₂	semidirect
27. #22563912	C₂	semidirect
28. #22563911	C₂	semidirect
33. C₂×#14524043	C₂²	semidirect
34. C₂×#14524042	C₂²	semidirect
35. C₂×#14524035	C₂²	semidirect
36. C₂×#14524034	C₂²	semidirect
48. #16863338	C₂²	semidirect
49. #16863338	C₂²	semidirect
50. #16863338	C₂²	semidirect
51. #16863338	C₂²	semidirect
52. #16863338	C₂²	semidirect
53. #16863338	C₂²	semidirect
54. #16863335	C₂²	semidirect
55. #16863335	C₂²	semidirect
60. #16863330	C₂²	semidirect
61. #16863330	C₂²	semidirect
62. #16863330	C₂²	semidirect
63. #16863330	C₂²	semidirect
64. #16863330	C₂²	semidirect
65. #16863330	C₂²	semidirect
66. #16863329	C₂²	semidirect
67. #16863329	C₂²	semidirect
68. #16863329	C₂²	semidirect
69. #16863329	C₂²	semidirect
70. #16863328	C₂²	semidirect
71. #16863328	C₂²	semidirect
72. #16863328	C₂²	semidirect
73. #16863328	C₂²	semidirect
74. #16863328	C₂²	semidirect
75. #16863328	C₂²	semidirect
84. #16863317	C₂²	semidirect
85. #16863317	C₂²	semidirect
86. #16863317	C₂²	semidirect
87. #16863317	C₂²	semidirect
88. #16863317	C₂²	semidirect
89. #16863317	C₂²	semidirect
90. #16863316	C₂²	semidirect
91. #16863316	C₂²	semidirect
96. #16863302	C₂²	semidirect
97. #16863302	C₂²	semidirect
98. #16863300	C₂²	semidirect
99. #16863300	C₂²	semidirect
100. #16863295	C₂²	semidirect
101. #16863295	C₂²	semidirect
102. #16863294	C₂²	semidirect
103. #16863294	C₂²	semidirect
104. #16863294	C₂²	semidirect
105. #16863294	C₂²	semidirect
106. #16863294	C₂²	semidirect
107. #16863294	C₂²	semidirect
108. #16863293	C₂²	semidirect
109. #16863293	C₂²	semidirect
110. #16863292	C₂²	semidirect
111. #16863292	C₂²	semidirect
120. #16863283	C₂²	semidirect
121. #16863283	C₂²	semidirect
122. #16863280	C₂²	semidirect
123. #16863280	C₂²	semidirect
124. #16863280	C₂²	semidirect
125. #16863280	C₂²	semidirect
126. #16863279	C₂²	semidirect
127. #16863279	C₂²	semidirect
152. #16863266	C₂²	semidirect
153. #16863265	C₂²	semidirect
154. #16863262	C₂²	semidirect
155. #16863261	C₂²	semidirect
332. C₂×C₂²⋊C₄×C₆₇	Q₈	semidirect
760. C₆₇	#36748	semidirect
1017. C₂×C₂²⋊C₄	Dic₁₃₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22568494	2
#22568176	2
#22567979	2
#22567974	2
#22567956	2
#22567952	2
#22567693	2
#22567690	2
#22567625	2
#22567335	2
#22567192	2
#22567188	2
#22567093	2
#22567086	2
#22566868	2
#22566864	2
#22566521	2
#22566018	2
#22565434	2
#22565428	2
#22565221	2
#22565215	2
#22563934	2
#22563933	2
#22563912	2
#22563911	2
#22562807	2
C₂×#16863271	2
C₆₇×#2312	2
#36748	67